There are extensive discussions on this forum for carrying and using a digital audio recorder in protection against false accusations. There is not a recommendation to video record anything here. Specific equipment has been discussed in the technology forum, but members would be happy to discuss their own experience here in your thread. Everyone deserves attention, and not to be referred to a pinned thread.
Certainly, if it is known that the mother is violent toward the children, you do not record it - you remove the children from the potential risk of violence. Perhaps you would like to explain what you intend to record and for what purpose?
Also, what State do you reside in?
Volenti non fit injuria